| /* Split a double into fraction and mantissa. |
| Copyright (C) 2007-2021 Free Software Foundation, Inc. |
| |
| This program is free software: you can redistribute it and/or modify |
| it under the terms of the GNU General Public License as published by |
| the Free Software Foundation; either version 3 of the License, or |
| (at your option) any later version. |
| |
| This program is distributed in the hope that it will be useful, |
| but WITHOUT ANY WARRANTY; without even the implied warranty of |
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| GNU General Public License for more details. |
| |
| You should have received a copy of the GNU General Public License |
| along with this program. If not, see <https://www.gnu.org/licenses/>. */ |
| |
| /* Written by Paolo Bonzini <bonzini@gnu.org>, 2003, and |
| Bruno Haible <bruno@clisp.org>, 2007. */ |
| |
| #if ! defined USE_LONG_DOUBLE |
| # include <config.h> |
| #endif |
| |
| /* Specification. */ |
| #include <math.h> |
| |
| #include <float.h> |
| #ifdef USE_LONG_DOUBLE |
| # include "isnanl-nolibm.h" |
| # include "fpucw.h" |
| #else |
| # include "isnand-nolibm.h" |
| #endif |
| |
| /* This file assumes FLT_RADIX = 2. If FLT_RADIX is a power of 2 greater |
| than 2, or not even a power of 2, some rounding errors can occur, so that |
| then the returned mantissa is only guaranteed to be <= 1.0, not < 1.0. */ |
| |
| #ifdef USE_LONG_DOUBLE |
| # define FUNC frexpl |
| # define DOUBLE long double |
| # define ISNAN isnanl |
| # define DECL_ROUNDING DECL_LONG_DOUBLE_ROUNDING |
| # define BEGIN_ROUNDING() BEGIN_LONG_DOUBLE_ROUNDING () |
| # define END_ROUNDING() END_LONG_DOUBLE_ROUNDING () |
| # define L_(literal) literal##L |
| #else |
| # define FUNC frexp |
| # define DOUBLE double |
| # define ISNAN isnand |
| # define DECL_ROUNDING |
| # define BEGIN_ROUNDING() |
| # define END_ROUNDING() |
| # define L_(literal) literal |
| #endif |
| |
| DOUBLE |
| FUNC (DOUBLE x, int *expptr) |
| { |
| int sign; |
| int exponent; |
| DECL_ROUNDING |
| |
| /* Test for NaN, infinity, and zero. */ |
| if (ISNAN (x) || x + x == x) |
| { |
| *expptr = 0; |
| return x; |
| } |
| |
| sign = 0; |
| if (x < 0) |
| { |
| x = - x; |
| sign = -1; |
| } |
| |
| BEGIN_ROUNDING (); |
| |
| { |
| /* Since the exponent is an 'int', it fits in 64 bits. Therefore the |
| loops are executed no more than 64 times. */ |
| DOUBLE pow2[64]; /* pow2[i] = 2^2^i */ |
| DOUBLE powh[64]; /* powh[i] = 2^-2^i */ |
| int i; |
| |
| exponent = 0; |
| if (x >= L_(1.0)) |
| { |
| /* A positive exponent. */ |
| DOUBLE pow2_i; /* = pow2[i] */ |
| DOUBLE powh_i; /* = powh[i] */ |
| |
| /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, |
| x * 2^exponent = argument, x >= 1.0. */ |
| for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); |
| ; |
| i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) |
| { |
| if (x >= pow2_i) |
| { |
| exponent += (1 << i); |
| x *= powh_i; |
| } |
| else |
| break; |
| |
| pow2[i] = pow2_i; |
| powh[i] = powh_i; |
| } |
| /* Avoid making x too small, as it could become a denormalized |
| number and thus lose precision. */ |
| while (i > 0 && x < pow2[i - 1]) |
| { |
| i--; |
| powh_i = powh[i]; |
| } |
| exponent += (1 << i); |
| x *= powh_i; |
| /* Here 2^-2^i <= x < 1.0. */ |
| } |
| else |
| { |
| /* A negative or zero exponent. */ |
| DOUBLE pow2_i; /* = pow2[i] */ |
| DOUBLE powh_i; /* = powh[i] */ |
| |
| /* Invariants: pow2_i = 2^2^i, powh_i = 2^-2^i, |
| x * 2^exponent = argument, x < 1.0. */ |
| for (i = 0, pow2_i = L_(2.0), powh_i = L_(0.5); |
| ; |
| i++, pow2_i = pow2_i * pow2_i, powh_i = powh_i * powh_i) |
| { |
| if (x < powh_i) |
| { |
| exponent -= (1 << i); |
| x *= pow2_i; |
| } |
| else |
| break; |
| |
| pow2[i] = pow2_i; |
| powh[i] = powh_i; |
| } |
| /* Here 2^-2^i <= x < 1.0. */ |
| } |
| |
| /* Invariants: x * 2^exponent = argument, and 2^-2^i <= x < 1.0. */ |
| while (i > 0) |
| { |
| i--; |
| if (x < powh[i]) |
| { |
| exponent -= (1 << i); |
| x *= pow2[i]; |
| } |
| } |
| /* Here 0.5 <= x < 1.0. */ |
| } |
| |
| if (sign < 0) |
| x = - x; |
| |
| END_ROUNDING (); |
| |
| *expptr = exponent; |
| return x; |
| } |